Because if the mirror had eyes, us flipped is what it would see. Just like if someone stands in front of you, looking at you, his left arm is on your right side. What would be weird is if the mirror showed us not flipped.

He means that when you look in a mirror while brushing you teeth, you see the mirror's reflection of you. But if someone were to look at you, it would be a flipped version of what you see in the mirror.